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Identities of finitely generated algebras over an infinite field

A. R. Kemer


Abstract: It is proved that for each finitely generated associative PI-algebra $U$ over an infinite field $F$, there is a finite-dimensional $F$-algebra $C$ such that the ideals of identities of the algebras $U$ and $C$ coincide. This yields a positive solution to the local problem of Specht for algebras over an infinite field: A finitely generated free associative algebra satisfies the maximum condition for $T$-ideals.

UDC: 512.552.4

MSC: Primary 16A06, 16A38; Secondary 16A46

Received: 13.02.1989

 English version: Mathematics of the USSR-Izvestiya, 1991, 37:1, 69–96

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